Question 1

Michelle Adams is deciding on one of two career choices, before retiring in 20 year time.

Choice 1

Michelle can go to a prestigious graduate school for two years and obtain a degree. Including tuition and living expenses, she expects to pay $35,000 at the end of each year for two years while at school. After graduating, she expects to land a demanding job that pays $90,000 at the end of the third year, and grows at a constant rate of 5% each year (so at the end of the fourth year she expects 90,000*1.05=$94,500 etc.) She will retire in 18 years after finishing graduate school.

Choice 2

Michelle can continue in her present job. She expects to be paid $42,000 at the end of the year, and expects her salary to increase by 10% every year, paid at the end of each year. She expects to work 20 years before retiring.

a.Make a time line with cash flows for Michelle's first choice.

b.Make a time line with cash flows for Michelle's second choice.

c.Suppose Michelle's discount rate is 12%. Which career should she choose?

Question 2

Consider the following risk-free T-bill and coupon bonds available for sale in the bond market (annual coupons):

Maturity

Price

Coupon

1

942

T-bill

2

995

6.3%

3

998

7.5%

4

985.25

6.75%

a) Your company plans to issue four-year maturity bonds. You plan to issue bonds priced at $980. At what level should you plan to set the coupon on your bond?

b) Suppose now that your company does not have money to pay coupons, and thus plans rather to issue discount bonds instead of coupon bonds. At what price do you expect to sell the zero-coupon bonds?

Question 3

Assume that stocks in this economy are priced according to CAPM. You are holding a portfolio of stocks where the beta of your portfolio is 1.5 and its correlation with the market portfolio is 0.75. The risk-free rate is 5%, the expected market return is 10%, and the standard deviation of the market return is 15%.

a.Is your current portfolio efficient? Explain.

b.How much additional expected return can you earn (without increase in total risk) if you make your portfolio efficient.

Question 4

An at the money 3-month call option on the SPX index is currently trading at $52.82 on CBOE. An investor wishes to price a 3-month put option on the SPX. Suppose the SPX is currently at 1400, and the put is also at the money (i.e. currently the price of the index is exactly the same as the exercise price of the option written on this index.) Take the volatility of the return on SPX to be 15% and the risk-free rate to be 6%. Find the price of the this put option.

Question 5

The common stock of Sternco is currently trading at $40 per share. Sternco is currently "in play" as a take-over target and is not expected to pay any dividends for the next 6 months. You believe that if management is successful at repelling all offers, the stock price will fall significantly, but if they are unsuccessful, the stock price will rise significantly. You want to profit from either outcome. The risk-free rate is 10% and a 6-month put option with an exercise price of $40 is selling at $4.

1. A dealer offers you a 6-month European call option with an exercise price of $40. What is a fair price for this option?
2. Propose a strategy to take advantage of your beliefs that uses the above mentioned put and call options. That is the strategy that allows you to profit from both: the significant price increase and decrease. Your answer should include the payoff table and graph.

Question 6

The stock of Nogro Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue indefinitely.

a.Assuming the current market price of the stock reflects its value, what rate of return do Nogro's investors require?

b.By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested?

c.What is the PVGO for this company?

d.If Nogro were to cut its dividend payout ratio to 25%, what would happen to its stock price?

e.What did you notice about the relationship between Nogro's dividend payout policy and its price?

f.What do you think is the reason for such relationship?